GATE DA 2026 Set 1 — Question 20
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Probability & Statistics → Counting → Combinations
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Question
Suppose that a computer program provides a non-negative and integer-valued random solution to the equation .Which of the following is the probability that all of in the provided solution are positive?
Correct answer
(A) 193233
Solution
The equation is , where and .
The total number of non-negative integer solutions is given by the formula , where and :
Total solutions = .We want to find the number of solutions where all are positive ().
Let , where . Substituting this into the equation:
The number of non-negative integer solutions for is:
Positive solutions = .The probability is the ratio of positive solutions to total solutions:
.Thus, option (A) is correct.
The total number of non-negative integer solutions is given by the formula , where and :
Total solutions = .We want to find the number of solutions where all are positive ().
Let , where . Substituting this into the equation:
The number of non-negative integer solutions for is:
Positive solutions = .The probability is the ratio of positive solutions to total solutions:
.Thus, option (A) is correct.
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